Composition and splitting are useful techniques for constructing special purpose integration methods for numerically solving many types of differential equations. In this ...

The package Summa.m provides a few basic functions that allow the user to handle sums with symbolic, infinite, and numerical endpoints without having Mathematica evaluate ...

This is a one-semester course on mathematical methods of physics normally taken by graduate students. The primary topics include: theory of analytic functions, integration ...

A fast method of modeling spectral lines is presented. The method utilizes a new approach in generating the Voigt profile using Mathematica. As an example, we consider the ...

This book examines various mathematical tools--based on generalized collocation methods--to solve nonlinear problems related to partial differential and integrodifferential ...

Let f be a function f: R -> R and zeta a root of f, that is, f(zeta)=0. It is well known that if we take x_0 close to zeta, and under certain conditions that I will not ...

In this paper, we describe a high-precision validation method for the solution of initial value problems (IVP's) of ordinary differential equations with the Taylor model. ...

This package provides Mathematica functions for resampling a statistic of a univariate random variable in parametric and nonparamteric modes and for computation of confidence ...

A survey of the many methods used to approximate Pi. For example, pictured here is the Pie Wedge method.

Perturbation–iteration method is generalized for systems of first order differential equations. Approximate solutions of Lotka–Volterra systems are obtained using the ...